Existence of global strong solutions in critical spaces for barotropic viscous fluids

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension $N\geq2$. We address the question of the global existence of strong solutions for initial data close from a constant state having critical Besov regularity. In a first time, this article show the recent results of \cite{CD} and \cite{CMZ} with a new proof. Our result relies on a new a priori estimate for the velocity, where we introduce a new structure to \textit{kill} the coupling between the density and the velocity as in \cite{H2}. We study so a new variable that we call effective velocity. In a second time we improve the results of \cite{CD} and \cite{CMZ} by adding some regularity on the initial data in particular $\rho_{0}$ is in $H^{1}$. In this case we obtain global strong solutions for a class of large initial data on the density and the velocity which in particular improve the results of D. Hoff in \cite{5H4}. We conclude by generalizing these results for general viscosity coefficients

Effective lagrangian for a mass dimension one fermionic field in curved spacetime

In this work we use momentum-space techniques to evaluate the propagator $G(x,x^{\prime})$ for a spin $1/2$ mass dimension one spinor field on a curved Friedmann-Robertson-Walker spacetime. As a consequence, we built the one-loop correction to the effective lagrangian in the coincidence limit. Going further we compute the effective lagrangian in the finite temperature regime. We arrive at interesting cosmological consequences, as time-dependent cosmological `constant', fully explaining the functional form of previous cosmological models.Comment: 9 pages, 0 figure

Some remarks on the attractor behaviour in ELKO cosmology

Recent results on the dynamical stability of a system involving the interaction of the ELKO spinor field with standard matter in the universe have been reanalysed, and the conclusion is that such system does not exhibit isolated stable points that could alleviate the cosmic coincidence problem. When a constant parameter $\delta$ related to the potential of the ELKO field is introduced in the system however, stable fixed points are found for some specific types of interaction between the ELKO field and matter. Although the parameter $\delta$ is related to an unknown potential, in order to satisfy the stability conditions and also that the fixed points are real, the range of the constant parameter $\delta$ can be constrained for the present time and the coincidence problem can be alleviated for some specific interactions. Such restriction on the ELKO potential opens possibility to apply the ELKO field as a candidate to dark energy in the universe, and so explain the present phase of acceleration of the universe through the decay of the ELKO field into matter.Comment: 17 pages, section III with minor changes and section IV rewritten with a new analysi

Questing for Algebraic Mass Dimension One Spinor Fields

This work deals with new classes of spinors of mass dimension one in Minkowski spacetime. In order to accomplish it, the Lounesto classification scheme and the inversion theorem are going to be used. The algebraic framework shall be revisited by explicating the central point performed by the Fierz aggregate. Then the spinor classification is generalized in order to encompass the new mass dimension one spinors. The spinor operator is shown to play a prominent role to engender the new mass dimension one spinors, accordingly.Comment: 7 pages, final version to appear in Eur. Phys. J.

On the bilinear covariants associated to mass dimension one spinors

In this paper we approach the issue of Clifford algebra basis deformation, allowing for bilinear covariants associated to Elko spinors which satisfy the Fierz-Pauli-Kofink identities. We present a complete analysis of covariance, taking into account the involved dual structure associated to Elko. Moreover, the possible generalizations to the recently presented new dual structure are performed.Comment: 9 pages, 0 figure

TWO NEW SPECIES OF GASTROPTERIDAE FROM GUAM, MARIANAS ISLANDS (OPISTHOBRANCHIA : CEPHALASPIDEA)

In 1964 Tokioka and Baba established the genus Sagaminopteron to accommodate one species, S. ornatum Tokioka and Baba, 1964. According to Tokioka and Baba Sagaminopteron differs from the Gastropteron in that the former has a radular formula of 9-12.1.0.1.9-12 with the first lateral having two prominent cusps on the inner edge of the main hook, whereas the latter has a radular formula of 4-6.1.0.1.4-6 and denticulations on the inner edge of the main hook of the first lateral. On the basis of these generic characteristics and external comparative descriptions with S. ornatum two new species have been identified from Guam: Sagaminopteron nigropunctatum and S. bilealbum. All external descriptions are from the living animals. We wish to thank Dr. Willard Hartman of the Peabody Museum of Natural History, Yale University, for identification of the sponges involved

On the Spinor Representation

A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz-Pauli-Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein, for instance, the first and second homotopy groups play prominent roles on the underlying physical properties, associated to the fermionic fields.Comment: 16 page

Experimental Constraints on a Vesta Magma Ocean

A magma ocean model was devised to relate eucrites (basalts) and diogenites (orthopyroxenites), which are found mixed together as clasts in a suite of polymict breccias known as howardites. The intimate association of eucritic and diogenitic clasts in howardites argues strongly that these three classes of achondritic meteorites all originated from the same planetoid. Reflectance spectral evidence (including that from the DAWN mission) has long suggested that Vesta is indeed the Eucrite Parent Body. Specifically, the magma ocean model was generated as follows: (i) the bulk Vesta composition was taken to be 0.3 CV chondrite + 0.7 L chondrite but using only 10% of the Na2O from this mixture; (ii) this composition is allowed to crystallize at 500 bar until approx. 80% of the system is solid olivine + low-Ca pyroxene; (iii) the remaining 20% liquid crystallizes at one bar from 1250C to 1110C, a temperature slightly above the eucrite solidus. All crystallization calculations were performed using MELTS. In this model, diogenites are produced by cocrystallization of olivine and pyroxene in the >1250C temperature regime, with Main Group eucrite liquids being generated in the 1300-1250C temperature interval. Low-Ca pyroxene reappears at 1210C in the one-bar calculations and fractionates the residual liquid to produce evolved eucrite compositions (Stannern Trend). We have attempted to experimentally reproduce the <1250C portion of the MELTS Vesta magma ocean. In the MELTS calculation, the change from 500 bar to one bar results in a shift of the olivine:low-Ca pyroxene boundary so that the 1250C liquid is now in the olivine field and, consequently, olivine should be the first-crystallizing phase, followed by low-Ca pyroxene at 1210C, and plagioclase at 1170C. Because at one bar the olivine:low-Ca pyroxene boundary is a peritectic, fractional crystallization of the 1210C liquid proceeds with only pyroxene crystallization until plagioclase appears. Thus, the predictions of the MELTS calculation are clear and straightforward

A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations

In this paper, we obtain a blow up criterion for classical solutions to the 3-D compressible Naiver-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, initial vacuum is allowed in our case.Comment: 25 page